Conductors, Insulators, and Semiconductors

Copper carries current, glass and plastic keep it where it belongs, and silicon can be made to do almost anything in between. This article explains why, starting from what the electrons inside each material are doing, and ends with how a few impurity atoms turn silicon into the raw material of every diode and transistor.

No background is assumed: every technical word is explained the first time it appears, and recap links point back to the first article where helpful.

1. A short recap: valence electrons

From What is Electronics:

• Atoms have a small positive nucleus surrounded by negative electrons arranged in shells. The outermost electrons, the valence electrons, are held most loosely and decide how a material behaves. (Recap: the valence shell.)
• Copper has one valence electron. Silicon (Si) and germanium (Ge) have four.
• Two atoms sharing a pair of electrons form a covalent bond. In a silicon crystal each atom bonds to four neighbors, so each is surrounded by eight shared electrons.^[1]
• In a metal the valence electrons leave their atoms and roam the whole piece as a "sea" of shared electrons.^[2] (Recap: why valence electrons decide.)

A conductor lets electric charge move easily, an insulator almost completely blocks it, and a semiconductor sits in between, with a conductivity very sensitive to temperature, light and tiny amounts of impurities.^[3] Anything that carries charge through a material, such as a free electron, is a charge carrier.

2. Energy bands, step by step

From energy levels to energy bands

The energy of a single electron is measured in electron volts (eV): 1 eV = 1.60 × 10⁻¹⁹ joule.^[4] An electron in a lone atom can only have certain fixed energies, called energy levels.

A crystal is different. A sugar-cube-sized piece of silicon (one cubic centimeter, cm³) holds about 5 × 10²² atoms.^[5] Packed that close, the atoms disturb each other's electrons, and each sharp level spreads into a broad range of closely spaced levels called an energy band. Between the bands are energies no electron in the crystal can have.^[3]

• The valence band is the highest band that is completely full when the material is cold. In silicon these are the electrons holding the bonds together.^[3]
• The conduction band is the next band up. An electron there is not tied to a bond and can move through the crystal.^[3]
• The band gap is the forbidden range between them. In chemical terms, it is the energy needed to free an electron from a covalent bond.^[6]

Why a full band carries no current

To carry current, an electron must pick up a little energy from the applied voltage and move into a slightly higher-energy state. The Pauli exclusion principle says no two electrons can occupy the same state,^[7] so in a full band there is nowhere to go: every nearby state is taken.^[8] Current needs a partly empty band, or electrons lifted into the empty conduction band.

How much energy does heat provide?

Temperature measures how hard the atoms are jiggling. The kelvin (K) scale starts at absolute zero, about −273 °C,^[9] with steps the same size as Celsius degrees, so room temperature is about 300 K. At 300 K the typical thermal energy, written kT, is only about 0.026 eV.^[8] Silicon's gap of about 1.12 eV^[3] is roughly 43 times that, so only a rare, unusually large jolt frees an electron. Diamond's 5.5 eV gap^[3] is about 210 times kT, and at room temperature essentially no electrons cross it.

The Fermi level, in plain terms

Fill the available electron states one at a time from the lowest energy up, as happens at absolute zero. The energy of the highest filled state is the Fermi level.^[8] At room temperature the edge blurs only slightly: states well below it are almost certainly full and states well above it almost certainly empty.^[8]

• In a metal the Fermi level lies inside a band (about 7 eV up in copper), so empty states sit right beside the filled ones and the slightest voltage moves electrons.^[8]
• In a pure semiconductor or insulator it falls in the gap, where there are no states at all. It simply marks that the band below is full and the band above nearly empty.^[8]
• Doping (section 10) moves it up toward the conduction band or down toward the valence band.^[8]

3. Electron-hole pairs

When heat or light breaks a bond in pure silicon, the freed electron jumps to the conduction band and can move. The bond it left is one electron short, and that vacancy is a hole.^[3]​^[10] Created together, they form an electron-hole pair, and creating one is called generation.

An electron from a neighboring bond can hop into the hole, leaving a new hole behind. So the hole moves opposite to the electrons that fill it and behaves like a positive charge traveling through the crystal. Both free electrons and holes carry current.^[3]​^[10] Electrons are the faster of the two: in pure silicon they are about three times as mobile as holes.^[3]

The reverse also happens constantly. A free electron that meets a hole drops back into it and both disappear, which is called recombination. At a steady temperature, generation and recombination balance.^[5]​^[11] In silicon the energy released ends up mostly as heat.^[12]

A pure semiconductor is called intrinsic. In it, free electrons and holes are equal in number, and that number is the intrinsic carrier concentration, n_i.^[13] At room temperature it is about 2 × 10⁶ per cm³ in gallium arsenide, 1 × 10¹⁰ in silicon and 2 × 10¹³ in germanium.^[6] The smaller the gap, the more carriers (germanium's gap is only about 0.66 eV^[14]). Even so, silicon's 10¹⁰ means only about one broken bond per five trillion atoms,^[5] which is why pure silicon conducts poorly.

4. Conductors

In a metal the Fermi level lies inside a band, so free electrons with empty states beside them are always present, at any temperature.^[8] Copper is modeled as having about one free electron per atom.^[15] What limits the current is resistance, measured in ohms (Ω) (recap): moving electrons collide with the vibrating atoms and with impurities.^[16] To compare materials, engineers use resistivity (ρ, "rho"), a property of the material itself. A wire's resistance is R = ρL/A, where L is its length and A its cross-sectional area. Resistivity is measured in ohm-meters (Ω·m), and lower means a better conductor.^[16]

Resistivities from OpenStax College Physics 2e, Table 20.1.^[16]

Graphite is the odd one out. It is carbon arranged in flat sheets. Each atom bonds to three neighbors, and its fourth valence electron spreads across the whole sheet, free to move within it.^[20] Diamond, by contrast, uses all four electrons in bonds and insulates.^[20] Because the sheets do not share their mobile electrons, graphite conducts far better along the sheets than across them.^[20] Its resistance also falls slightly as it warms, unlike a metal, which is why OpenStax files carbon under semiconductors.^[16] In practice it is a usable but mediocre conductor.

5. Insulators

In an insulator every valence electron is firmly held in a bond or a full shell, and the gap is large (diamond's is 5.5 eV).^[3] In diamond and quartz all the electrons are held tightly between atoms.^[20] Most solids are insulators.^[21]

• Glass: 10⁹ to 10¹⁴ Ω·m, and fused quartz about 7.5 × 10¹⁷,^[16] roughly 10¹⁷ to 10²² times copper's resistivity.
• Rubber and plastics: hard rubber 10¹³ to 10¹⁶ Ω·m. Teflon and Lucite (acrylic) are above 10¹³.^[16] Nylon and polystyrene are also common.^[22]
• Ceramics: traditionally insulating. Uses include spark plugs and protective beads and tubing for bare wires and power lines.^[23] Alumina (aluminum oxide) is made in bulk for insulators and spark plugs.^[18] The mineral mica measures 10¹¹ to 10¹⁵ Ω·m.^[16]
• Air: gases are generally good insulators,^[24] within limits (section 9).
• Dry wood: 10⁸ to 10¹¹ Ω·m.^[16] Dry matters: wood's resistance "decreases greatly as moisture content increases," which is exactly what wood-moisture meters measure.^[25]

6. Semiconductors

Semiconductors have small gaps, between about 0.25 and 2.5 eV for most important ones.^[3] At absolute zero every bond in pure silicon is intact and nothing conducts.^[11] At room temperature a few bonds break, and conductivity then changes dramatically with temperature, light and impurities.^[3] Some semiconductors are single elements from column IV of the periodic table, now numbered group 14 (Si, Ge). Others are compounds, such as gallium arsenide (GaAs), which pairs gallium from column III with arsenic from column V.^[3]

Published band gaps vary slightly with temperature and method. SiC comes in several crystal forms; ORNL lists 4H at 3.26 eV and 6H at 3.03 eV.^[26]

SiC and GaN are wide-bandgap semiconductors: their gaps are far larger than silicon's,^[26] so heat generates far fewer stray carriers and they keep working where silicon would fail.^[27] The gap also sets the color of light a semiconductor can emit. When an electron falls back across the gap, the energy can leave as a photon (a particle of light). Red light needs about 1.77 eV per photon and violet about 3.1 eV,^[12] which is why blue LEDs needed a wide-gap material like GaN.

7. Side by side

Sources: OpenStax (resistivities),^[16] Britannica and HyperPhysics (bands),^[3]​^[8] ORNL (wide-gap values).^[26] The boundaries between classes are not sharp.

8. Temperature changes everything

Metals: hotter means more resistance

For modest changes, R = R₀(1 + αΔT). Here R₀ is the starting resistance, ΔT the temperature change and α (alpha) the temperature coefficient of resistivity. For copper α is about +0.0039 per °C,^[16] so a copper winding warming from 20 °C to 70 °C gains about 20% in resistance. The number of free electrons barely changes, but the atoms vibrate harder, so the electrons collide more often.^[16]

Semiconductors: hotter means less resistance

In a pure semiconductor, heat breaks more bonds, and the extra carriers far outweigh the extra collisions.^[16] The carrier count grows exponentially with temperature.^[5] It roughly doubles for every 13 °C rise in germanium and every 8 °C in silicon.^[8] OpenStax gives α as about −0.07 per °C for pure silicon and −0.05 for germanium, where the minus sign means resistance falls as temperature rises.^[16]

Doped semiconductors (section 10) can behave differently. Their carrier count is set mainly by the impurities,^[28] while mobility falls with temperature,^[3] so their resistance can rise instead. Silicon PTC sensors called silistors rely on this.^[29]

Insulators: same physics, tiny numbers

Heat lifts electrons across an insulator's gap too, more of them the hotter it gets,^[8] but with a gap of several eV the number stays vanishingly small. In practice moisture is often the bigger threat, as damp wood shows.^[25]

Putting it to work: thermistors

A thermistor is a resistor designed to change resistance strongly with temperature, so its resistance reveals its temperature.^[16] There are two types:^[29]

• NTC (negative temperature coefficient): resistance falls as temperature rises. Most are ceramic. They are the most widely used type, for temperature monitoring, thermal protection and inrush-current limiting.^[29] As an inrush limiter, a cold NTC's high resistance tames the surge at switch-on, then drops as current warms it.
• PTC (positive temperature coefficient): resistance rises with temperature. Linear types, such as silistors, rise smoothly (about 0.6 to 0.8% per kelvin) and are used for sensing. Switching types jump sharply above a threshold temperature and are used for current limiting and thermal protection.^[29]

Superconductors: resistance that vanishes

In 1911 Heike Kamerlingh Onnes cooled mercury with liquid helium. Near 4.2 K (−269 °C) its resistance dropped abruptly to zero.^[7] This is superconductivity, and it begins below a material's critical temperature. A superconductor is not just a very good conductor. It is a different state of the material, which also expels magnetic fields (the Meissner effect, first seen in 1933).^[9] Currents in superconducting loops have kept flowing for years with no voltage source.^[7] In the standard theory (BCS, 1957), electrons pair up through the vibrating crystal and move in a coordinated way that ordinary collisions cannot disrupt.^[9]​^[7] Oddly, copper, silver and gold never superconduct.^[7]

In 1986 Georg Bednorz and Alex Müller found superconductivity in a copper-oxide ceramic. Within months others passed 90 K, cold enough to need only liquid nitrogen rather than liquid helium.^[9] One example is YBCO (yttrium barium copper oxide), with a critical temperature of 92 K.^[7] Room-temperature superconductivity remains a goal, not a reality. Today superconductors serve where the cooling pays off: MRI and particle-accelerator magnets, and ultra-sensitive magnetic sensors called SQUIDs.^[7]

9. When insulators fail: breakdown

Push hard enough and any insulator conducts. The push that matters is the electric field, the force per unit of charge at a given point, measured in volts per meter (V/m). Across a gap it is roughly the voltage divided by the gap width. The largest field a material withstands before it "begins to break down and conduct" is its dielectric strength.^[22] (A dielectric is an insulator used in an electric field, as in a capacitor.)

From OpenStax College Physics 2e, Table 19.1.^[22] Real values vary with thickness, purity, humidity and electrode shape.

A 1 mm air gap breaks down at about 3,000 V, while 1 mm of Teflon holds off about 60,000 V. Because the limit is a field, thinner insulation fails at a lower voltage.^[22]

How air breaks down. Air always holds a few stray free electrons. A strong field accelerates them, and one that gains roughly 10 eV before hitting a molecule knocks another electron loose. This is impact ionization, and it leaves behind an ion, a molecule with a net charge.^[24] Each freed electron is accelerated in turn and frees more, so their number multiplies. The air becomes a plasma, a glowing gas full of free charges, and you get a spark or arc, as in a static shock, a spark plug or an arc welder.^[24]

Lightning is the same thing on a giant scale. Collisions between ice and hail in a storm separate charge. Air insulates between the charged regions until the difference grows too great, then breaks down in a rapid discharge that can heat the air to about 50,000 °F, and the expanding air is the thunder.^[30] Dielectric strength is also why every capacitor and cable carries a voltage rating.

10. Doping: making n-type and p-type

Pure silicon is rarely used as it is. It is almost always doped,^[13] meaning tiny, controlled amounts of chosen impurity atoms (dopants) are added. These take the place of silicon atoms in the crystal.^[6] The effect is large: about 10 boron atoms per million silicon atoms can raise conductivity a thousandfold.^[3] Doping is older than the transistor. The crystal rectifiers in World War II radar receivers were silicon or germanium doped with traces of boron or phosphorus.^[31]

The choice depends on valence electrons. Periodic-table columns, called groups, are numbered 1 to 18. Older books use III, IV and V for groups 13, 14 and 15.^[18]​^[3] Silicon and germanium are in group 14.

n-type: donors add electrons

A group 15 atom, phosphorus (P), arsenic (As) or antimony (Sb), has five valence electrons. Four form the usual bonds, and the fifth is only weakly held.^[32]​^[3] Freeing it takes only about 0.045 eV for P, 0.054 for As and 0.039 for Sb, against 1.12 eV to break a silicon bond, so at room temperature practically all of them let go.^[6] These atoms are donors, and the result is n-type silicon ("n" for the negative carriers).^[3] Each donor adds a level just below the conduction band,^[33] and the Fermi level moves up.^[8]

p-type: acceptors create holes

A group 13 atom, boron (B), gallium (Ga) or indium (In) (aluminum also works), has only three valence electrons, so one bond is an electron short: a hole.^[32]​^[33] A neighboring electron moves in for about 0.045 eV (boron) to 0.072 eV (gallium). Indium needs about 0.16 eV,^[6] so in silicon fewer indium atoms are active at room temperature. The hole then wanders off and carries current. These atoms are acceptors, giving p-type silicon ("p" for positive holes).^[3] Each adds a level just above the valence band,^[33] and the Fermi level moves down.^[8] The same donors and acceptors work in germanium.^[33]

How much dopant? Useful concentrations in silicon run from about 10¹⁵ to 10²⁰ atoms per cm³, so even the heaviest doping replaces under 1% of the atoms.^[6]​^[11] Against 5 × 10²² silicon atoms per cm³,^[5] that is about one dopant atom per 50 million (10¹⁵) down to one per 500 (10²⁰). Even 10¹⁵ donors gives 100,000 times the free electrons of pure silicon, which is why silicon's resistivity spans 2,300 Ω·m pure to 0.1 Ω·m and below when doped.^[16]

11. Majority and minority carriers

In doped material the more plentiful carrier is the majority carrier and the scarcer one the minority carrier.^[32] In n-type, electrons are the majority and holes the minority. In p-type it is the reverse. Heat still makes pairs, so minority carriers never vanish, but they are rare. At a steady temperature the law of mass action holds: n·p = n_i², where n is the free-electron and p the hole concentration. Adding more of one carrier makes the other rarer, because the extras recombine with it.^[28]

p-type silicon, 10¹⁷ acceptors per cm³:
holes p ≈ 10¹⁷; electrons n = (10¹⁰)² ÷ 10¹⁷ = 10³ per cm³

That MIT example^[11] gives a ratio of a hundred trillion to one. n-type works the same way, with the roles swapped,^[11] and heavier doping means fewer minority carriers.^[28] Minority carriers matter a great deal in diodes, transistors and solar cells.

Sources: PVEducation, HyperPhysics and Stanford EE 116.^[32]​^[8]​^[6]

12. Where this leads: the PN junction

Make p-type and n-type regions side by side in one crystal and the boundary is a PN junction, first identified in silicon in 1940.^[35] Carriers spread from where they are crowded to where they are scarce, a process called diffusion. Electrons diffuse from the n side into the p side and recombine with holes. That leaves the fixed ions unbalanced: positive on the n side, negative on the p side. Their charge creates an electric field that sweeps free carriers out and stops further migration. This thin, carrier-free zone is the depletion region, and its field creates a built-in voltage.^[34]​^[36]

• Diodes are essentially one junction. Current flows readily under forward bias, where the applied voltage helps electrons over the barrier, and is blocked under reverse bias.^[36]
• Transistors arrange doped regions so a signal on one terminal (base or gate) controls the current between the other two, to amplify or switch.^[31]
• Solar cells are large junctions. Light makes electron-hole pairs and the junction's field sweeps them apart to be collected as current.^[37]​^[38]
• LEDs push electrons across a junction to recombine with holes and release light (electroluminescence). Silicon and germanium junctions give mostly heat, so LEDs use GaAs, GaAsP, GaP or, for blue, GaN.^[12]

Coming up in this section: 3 Resistors (resistivity and temperature coefficients at work), 4 Capacitors (insulators as dielectrics and voltage ratings), 5 Coils (Inductors), 6 Diodes (the PN junction in action), 7 Transistors, and 8 Transformers.

The whole story in brief

• In a crystal, electron energies form bands: a filled valence band and an empty conduction band, separated by the band gap.
• Conductors have the Fermi level inside a band. Insulators have a gap too big for heat to bridge. Semiconductors have a small gap, so a few electrons cross it, each leaving a hole.
• Resistivity spans more than 25 powers of ten, from silver to fused quartz.
• Heat raises a metal's resistance but lowers a pure semiconductor's, and thermistors exploit both. Some materials superconduct below a critical temperature.
• An insulator breaks down above its dielectric strength (air: about 3 kV/mm). Lightning is air breaking down.
• Group 15 donors make n-type material (electrons are the majority carriers). Group 13 acceptors make p-type material (holes are the majority). The law n·p = n_i² keeps minority carriers rare.
• A PN junction and its depletion region are the basis of diodes, transistors, solar cells and LEDs.

Sources

All links were checked in October 2026. External links open in a new tab.

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