Conductors and Insulators
Learning Objectives
By the end of this page, you should be able to:
- Explain how band theory determines whether a material conducts, insulates, or does neither cleanly
- Calculate and interpret resistivity, conductivity, and temperature-dependent resistance changes
- Compare common conductors and insulators using resistivity, dielectric strength, and permittivity
- Identify the breakdown mechanisms that cause insulators to fail
- Apply conductor/insulator selection principles to PCB design, high-voltage insulation, and MOSFET gates
Quick Answer
Every electronic material can be classified by how readily it allows electric charge to flow. Conductors (like copper) have overlapping valence and conduction bands, so electrons move almost freely, giving very low resistivity (~10⁻⁸ Ω·m). Insulators (like PTFE or glass) have a large band gap (>3 eV), so virtually no electrons reach the conduction band under normal fields, giving very high resistivity (10⁸–10¹⁸ Ω·m). Between them sit semiconductors, whose conductivity can be deliberately controlled. This distinction underpins nearly every practical decision in circuit design: which metal to use for PCB traces, how thick an insulating layer must be to prevent breakdown, and why a MOSFET's gate oxide can only be made so thin before it leaks current.
The Physics: Band Theory of Solids
The behavior of a material as a conductor, semiconductor, or insulator is determined by its electronic band structure — specifically the relationship between the valence band (filled electron states) and the conduction band (energy levels where electrons can move freely), separated by the band gap.
| Material Type | Band Gap (Eg) | Behavior |
|---|---|---|
| Conductor | 0 eV (bands overlap) | Electrons in conduction band at room temperature; current flows readily |
| Semiconductor | 0.1–3 eV (small gap) | Few electrons in conduction band at room temperature; conductivity increases with temperature or doping |
| Insulator | >3 eV (large gap) | Conduction band empty at room temperature; electrons cannot jump the gap with normal electric fields |
Example band gaps: Silicon 1.12 eV, Germanium 0.67 eV, Gallium Arsenide 1.42 eV, Diamond 5.5 eV (insulator), SiO₂ ~9 eV (insulator).
Why It Matters: Band gap isn't an abstract number — it's the reason silicon transistors work at all. A 1.12 eV gap is small enough that room-temperature thermal energy and an applied voltage can push electrons across it in a controlled way, but large enough that the material doesn't just conduct all the time like a metal.
Common Misunderstanding: Students often picture the band gap as a physical "gap" electrons squeeze through. It's actually a forbidden range of energy — electrons cannot occupy those energy states at all. They must gain enough energy to jump entirely past the gap, not through it.
Conductors
What Makes a Good Conductor?
A conductor has overlapping valence and conduction bands — electrons are free to move throughout the material lattice even without applied energy. This "sea" or "cloud" of free electrons is called the Fermi gas of conduction electrons.
Key electrical property: Electrical Conductivity (σ)
σ = 1/ρ = J/E
Where:
- σ = conductivity (S/m, Siemens per metre)
- ρ = resistivity (Ω·m, ohm-metres)
- J = current density (A/m²)
- E = electric field (V/m)
Real-World Example: When you strip a copper wire and touch it to a battery terminal, current flows almost instantly because copper's free electrons need no activation energy — they're already in the conduction band, waiting for an electric field to push them.
Common Conductors and Their Resistivities
| Material | Resistivity ρ (Ω·m, at 20°C) | Key Use |
|---|---|---|
| Silver (Ag) | 1.59 × 10⁻⁸ | Best conductor; too expensive for most applications; RF contacts |
| Copper (Cu) | 1.72 × 10⁻⁸ | PCB traces, wiring, busbars — industry standard |
| Gold (Au) | 2.44 × 10⁻⁸ | Connector plating; corrosion resistance over conductivity |
| Aluminum (Al) | 2.82 × 10⁻⁸ | Power lines (lighter than copper); heatsinks |
| Tungsten (W) | 5.6 × 10⁻⁸ | Light bulb filaments; high melting point (3422°C) |
| Nichrome (NiCr) | ~1.1 × 10⁻⁶ | Resistance heating elements; toasters, hair dryers |
| Carbon/Graphite | ~3–60 × 10⁻⁵ | Pencil traces; electrodes; carbon resistors |
Temperature Coefficient of Resistance (TCR)
For metallic conductors, resistivity increases with temperature — more thermal vibration disrupts electron flow:
ρ(T) = ρ₀ × [1 + α(T − T₀)]
Where α = temperature coefficient (positive for metals, e.g., copper α ≈ 0.00393 /°C).
Implication: A copper wire at 100°C has ~30% higher resistance than at 20°C. This matters for power cables, motor windings, and precision resistors.
Exception: Semiconductors and thermistors (NTC) have negative TCR — resistance decreases with temperature.
Superconductors: Below a critical temperature (e.g., mercury: 4.2 K, YBCO ceramic: 93 K), resistance drops to exactly zero. Used in MRI magnet coils, particle accelerators (CERN), and experimental power transmission.
Insulators
What Makes a Good Insulator?
An insulator has a large band gap — electrons are tightly bound in the valence band and cannot reach the conduction band under normal electric fields. There are virtually no free charge carriers.
Key electrical property: Dielectric Strength
Dielectric strength is the maximum electric field an insulator can withstand before breakdown (electrons forced into conduction band, current flows, material may be permanently damaged):
| Insulating Material | Dielectric Strength (kV/mm) | Relative Permittivity (εᵣ) | Key Use |
|---|---|---|---|
| Air (dry) | 3 kV/mm | 1.0 | Capacitor gap; gaps in HV equipment |
| Mica | 100–200 kV/mm | 4–8 | HF capacitors; high-temp insulation |
| Glass | 10–100 kV/mm | 5–10 | CRT, optical fiber cladding |
| PTFE (Teflon) | 60 kV/mm | 2.1 | RF coaxial cables; chemical resistance |
| Epoxy (PCB FR-4) | 15–25 kV/mm | 4.2–4.8 | PCB substrate; most common in electronics |
| Polyimide (Kapton) | 150–300 kV/mm | 3.5 | Flexible PCBs; aerospace wiring |
| Silicon dioxide (SiO₂) | 600–900 kV/mm | 3.9 | MOSFET gate oxide; 1–5 nm thick in modern chips |
| Rubber | 12–30 kV/mm | 2.5–4 | Wire insulation; safety gloves |
| PVC | 10–40 kV/mm | 3.5 | Most common wire jacket |
Real-World Example: A spark plug gap relies on air's ~3 kV/mm dielectric strength — engineers deliberately size the gap so that the ignition coil's voltage exceeds air's breakdown threshold at exactly the right moment, forcing a controlled spark.
Breakdown Mechanisms
- Avalanche breakdown: Free electrons accelerated by strong field ionize atoms → exponential carrier multiplication
- Thermal breakdown: Current → heat → more carriers → more current → thermal runaway
- Electrolytic breakdown: Moisture + ions migrate under DC field → gradual degradation (common in PCBs)
- Puncture vs. Flashover: Puncture = breakdown through material; Flashover = breakdown along surface (lower voltage)
Common Misunderstanding: Students often assume an insulator with high dielectric strength is automatically the "best" insulator for every job. In practice, mechanical flexibility, cost, thermal stability, and moisture resistance often outweigh raw dielectric strength — which is why PVC (only 10–40 kV/mm) remains the default wire jacket instead of mica (100–200 kV/mm).
Comparison: Conductors vs. Insulators vs. Semiconductors
| Property | Conductor | Semiconductor | Insulator |
|---|---|---|---|
| Free electrons at room temp | Many (~10²⁸/m³) | Few (~10¹⁶/m³ undoped Si) | Essentially none |
| Resistivity | 10⁻⁸ – 10⁻⁶ Ω·m | 10⁻⁴ – 10³ Ω·m | 10⁸ – 10¹⁸ Ω·m |
| Band gap | 0 eV (overlap) | 0.1–3 eV | >3 eV |
| Effect of temperature | Resistance increases | Resistance decreases | Minimal (until breakdown) |
| Effect of light | Minimal | Photoconductivity (photodiodes) | Minimal |
| Effect of doping | N/A | Dramatic — controls conductivity | N/A |
| Examples | Cu, Al, Au, Fe | Si, Ge, GaAs, InP | SiO₂, rubber, PTFE, air |
Practical Applications in Circuit Design
Conductor Selection in PCBs
Copper is the standard PCB conductor — 1 oz/ft² copper (~35 μm thick) for standard boards. Trace width and copper weight determine current-carrying capacity:
- A 1 mm trace in 1 oz copper: ~1.5 A maximum
- IPC-2221 standard provides trace width vs. current capacity tables
Gold plating on edge connectors: Gold doesn't oxidize, ensuring reliable mating contact over thousands of cycles.
Insulation Coordination in High-Voltage Design
IEC 60664 defines creepage (along surface) and clearance (through air) distances between conductors at different potentials, based on working voltage and pollution degree. Violating these causes arcing, fire, and electric shock.
Gate Oxide in MOSFETs
The gate of a MOSFET is separated from the channel by an insulating silicon dioxide (SiO₂) layer — now only 1–3 nm thick in advanced nodes (Intel, TSMC, Samsung). At these thicknesses, quantum mechanical tunneling causes gate leakage current — a key constraint driving development of high-κ dielectrics (HfO₂, Al₂O₃) as SiO₂ alternatives.
Key Terms
| Term | Definition |
|---|---|
| Resistivity (ρ) | Intrinsic material property describing opposition to current flow, in Ω·m |
| Conductivity (σ) | Reciprocal of resistivity; ease of current flow, in S/m |
| Band gap (Eg) | Forbidden energy range between valence and conduction bands, in eV |
| Dielectric strength | Maximum electric field an insulator withstands before breakdown, in kV/mm |
| Temperature coefficient of resistance (α) | Fractional change in resistance per degree of temperature change |
| Breakdown | Sudden onset of conduction in an insulator once the field exceeds dielectric strength |
| Creepage | Shortest path between two conductors measured along an insulating surface |
| Clearance | Shortest path between two conductors measured through air |
| Superconductor | Material with exactly zero resistance below a critical temperature |
Common Mistakes
Misconception 1: "The best conductor is always the right choice for a circuit." Why it's wrong: Cost, oxidation resistance, and mechanical properties often matter more than raw conductivity — silver conducts best but is rarely used for bulk wiring. Correct understanding: Material choice balances conductivity against cost, corrosion resistance, and mechanical needs (e.g., copper for traces, gold for connector plating).
Misconception 2: "Insulators never conduct at all." Why it's wrong: Every insulator has a breakdown voltage. Push the field high enough (avalanche, thermal, or electrolytic mechanisms) and any insulator will conduct, often destructively. Correct understanding: Insulators block current only within their rated dielectric strength; exceeding it causes breakdown.
Misconception 3: "All materials' resistance increases with temperature." Why it's wrong: This is true for metals (positive TCR) but false for semiconductors and NTC thermistors, which have negative TCR — resistance falls as temperature rises because more carriers are thermally excited into the conduction band. Correct understanding: Check whether the material is metallic or semiconducting before assuming the direction of the temperature effect.
Comparison and Connections
| Concept | Conductors | Insulators | Semiconductors |
|---|---|---|---|
| Governing property | High free-carrier density | Large band gap | Controllable carrier density |
| Temperature response | Resistance ↑ | Stable (until breakdown) | Resistance ↓ |
| Design use | Carrying current | Blocking/isolating current | Switching/amplifying current |
| Failure mode | Overheating, fusing | Dielectric breakdown | Thermal runaway, junction breakdown |
Practice Questions
Recall
- State the typical resistivity range (in Ω·m) for conductors, semiconductors, and insulators.
- Define dielectric strength and state its typical unit.
Understanding 3. Explain, using band theory, why copper conducts at room temperature but glass does not. 4. Why does a metal's resistance increase with temperature while a semiconductor's decreases?
Application 5. A PCB trace carrying 2 A needs to be sized using IPC-2221 guidance. Given that a 1 mm trace in 1 oz copper carries about 1.5 A, roughly how wide should the trace be, and what property of copper makes this calculation possible? 6. You're designing a high-voltage switch enclosure. Which two insulation parameters (besides dielectric strength) must you calculate to prevent arcing, per IEC 60664?
Analysis 7. Compare avalanche breakdown and thermal breakdown as failure mechanisms — which one is more likely in a fast-transient overvoltage event, and which is more likely under sustained overload? Justify your answer. 8. A MOSFET's gate oxide is shrunk from 5 nm to 1.5 nm to increase transistor density. Explain the trade-off this creates and why manufacturers are exploring high-κ dielectrics like HfO₂.
Answer Guidance: For Q5, scale the trace width roughly proportionally to current (about 1.3 mm for 2 A) and note that copper's low, stable resistivity is what makes width-based current tables reliable. For Q7, avalanche breakdown dominates under fast, high-field transients (electron multiplication is nearly instantaneous), while thermal breakdown builds up over time under sustained current. For Q8, tunneling leakage increases sharply as oxide thickness shrinks; high-κ dielectrics allow a physically thicker layer while keeping the same effective capacitance, reducing leakage.
FAQ
Q1: Why is copper used for PCB traces instead of silver, which conducts better? Copper offers over 95% of silver's conductivity at a small fraction of the cost, and it solders and etches well — the marginal conductivity gain from silver rarely justifies the price increase.
Q2: What actually happens physically during dielectric breakdown? The electric field becomes strong enough to rip electrons free from atoms in the insulator (or accelerate stray electrons enough to ionize others), creating a rapidly multiplying stream of charge carriers — the material briefly becomes a conductor, often permanently damaging it.
Q3: Why does a MOSFET gate need such an incredibly thin insulating layer? Thinner gate oxide gives stronger electrostatic control over the channel, letting transistors switch faster and pack more densely — but push it too thin and electrons "tunnel" straight through, causing leakage current even when the transistor should be off.
Q4: Are semiconductors insulators that got weaker, or conductors that got weaker? Neither — semiconductors are a fundamentally different class defined by a small but nonzero band gap that can be tuned via doping, temperature, or light. They aren't a "watered-down" version of either extreme.
Q5: Why do power lines use aluminum instead of copper, if copper conducts better? Aluminum is roughly one-third the weight of copper for the same resistance over long spans, and weight (and cost per kilometer) matters more than the raw conductivity difference for overhead transmission lines.
Quick Revision
- Conductors: 0 eV band gap, bands overlap, resistivity ~10⁻⁸–10⁻⁶ Ω·m.
- Insulators: >3 eV band gap, resistivity ~10⁸–10¹⁸ Ω·m.
- Semiconductors: 0.1–3 eV band gap, controllable via doping/temperature/light.
- σ = 1/ρ = J/E — conductivity is the reciprocal of resistivity.
- Metals have positive TCR (resistance ↑ with temperature); semiconductors/NTC thermistors have negative TCR.
- Superconductors reach exactly zero resistance below a critical temperature (e.g., mercury 4.2 K).
- Dielectric strength = maximum field an insulator withstands before breakdown (kV/mm).
- Four breakdown mechanisms: avalanche, thermal, electrolytic, and puncture/flashover.
- SiO₂ has extremely high dielectric strength (600–900 kV/mm) and is the classic MOSFET gate insulator.
- Creepage (along surface) and clearance (through air) govern high-voltage insulation design per IEC 60664.
- Copper dominates PCB traces and wiring due to cost-performance balance, not because it's the best conductor.
- Gold plating is chosen for connectors for oxidation resistance, not conductivity.
Related Topics
Prerequisites: Introduction to Electronic Materials; basic Ohm's Law.
Related Topics: Semiconductors; Dielectrics; Material Characterization.
Next Topics: Semiconductors (doping, p-n junctions, and how band gap is exploited to build active devices).