Solid State Physics

H3 solid state physics hub: a four-lesson path from energy bands through charge transport and Hall measurements to the Zener diode.

Advanced Physics

Learning goals

Connect energy bands, carrier response, Hall measurements, and semiconductor-device behaviour.

Solid state physics connects microscopic bonding and carrier models to macroscopic conductivity and device behaviour.

The four lessons move from energy bands to how carriers carry current, then to measuring carriers with the Hall effect, and finally to a semiconductor device.

Audience: Learners linking condensed-matter models to transport/device questions.

Prerequisites:

Learning path:

The earlier separate notes on current density, the Drude model, resistivity and conductor materials are now part of lesson 2.

Revision

Quick Reference

Current and current density: I = n|q|Av_d and J = nqv_d.
Drude conductivity: σ = nq²τ/m and ρ = 1/σ.
Resistivity relation: R = ρL/A.
Hall coefficient: R_H = 1/nq.
Fermi-Dirac: f(E) = 1/(exp((E-μ)/kT) + 1).

Problem Templates

Convert microscopic quantities with J = nqv_d, then connect to macroscopic I = JA.
In Hall problems, keep carrier sign explicit before interpreting material type.
In band problems, justify conductor/semiconductor behaviour with gap size and occupancy.

Practice

Each lesson has try-it tasks with worked answers. For examination-style questions, use the H3 paper map.

H3 Paper Map (9814)

Check what I know

Check what I know: Solid State Physics

A text-first Solid State Physics assessment with labelled response controls.

About 6 minutes

Check what I know

Answer 2 short questions. This starting check helps choose what to work on; it does not prove mastery.

Recent attempts

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This check needs JavaScript to record answers. The reviewed questions are listed below for study.

Silicon has a band gap of about $1.1\,\mathrm{eV}$ between its valence and conduction bands. Why is it classed as a semiconductor rather than an insulator at room temperature?

The gap is small enough that thermal energy excites a measurable number of electrons into the conduction band, leaving holes in the valence band.
The gap is zero, so the bands overlap as in a metal.
The gap is so large that no electrons can cross it, but the holes conduct.
Silicon atoms donate free electrons like a metal's conduction electrons.

A flat conductor carries a current in the $+x$ direction in a magnetic field along $+z$. A Hall voltage appears across the $y$-direction. What does the sign of this Hall voltage reveal?

The sign of the charge carriers: electrons and holes are deflected to the same edge but give opposite Hall voltages.
Nothing about the carriers; the sign depends only on the current direction.
The Hall voltage is always zero for hole conduction.
The carrier mass, because heavier carriers are deflected less.

Practise

Practise: Solid State Physics

A text-first Solid State Physics assessment with labelled response controls.

About 10 minutes

Practise

Questions are selected when you start. Use the feedback to decide what to practise next; this does not prove mastery.

Recent attempts

History is stored only in this browser.

No completed attempts are saved yet.

This check needs JavaScript to record answers. The reviewed questions are listed below for study.

In a material dominated by one type of mobile carrier, what information does the sign of the measured Hall coefficient provide?

The sign of the dominant charge carrier.
The magnitude of the material's band gap only.
Whether the sample has zero resistance.
The direction of conventional current, independent of carrier type.

Why can a correctly biased Zener diode stabilise a supply voltage over a range of currents?

In reverse breakdown, its terminal voltage remains approximately equal to the Zener voltage over that current range.
In forward bias, it forces the current to zero at every applied voltage.
Its resistance is exactly zero, so it removes all voltage from the load.
Its depletion layer prevents every reverse current from flowing.

A uniform metal wire has cross-sectional area 2.0 mm² and electron number density 8.0 × 10²⁸ m⁻³. Its conventional current is 4.8 A in the +x direction. Take the electron charge as −1.60 × 10⁻¹⁹ C. Calculate the signed x components of current density and electron drift velocity.

Current density Jₓ / A m⁻²
Electron drift velocity vₓ / m s⁻¹

In a Drude model, a metal has electron density 8.0 × 10²⁸ m⁻³, relaxation time 2.5 × 10⁻¹⁴ s and electron mass 9.11 × 10⁻³¹ kg. The electron charge is −1.60 × 10⁻¹⁹ C. A uniform field of +0.010 V m⁻¹ points along x. Find the conductivity, resistivity and signed electron drift velocity. Assume relaxation time is independent of field.

Conductivity / S m⁻¹
Resistivity / Ω m
Drift velocity vₓ / m s⁻¹

A uniform wire of length 2.0 m and circular diameter 0.50 mm has resistance 0.18 Ω. It is then drawn into a uniform wire twice as long, with the same volume. For this model, temperature and material resistivity remain unchanged. Determine the original resistivity and the new resistance.

Original resistivity / Ω m
Resistance after drawing / Ω

Illustrative measurements on a metal sample are shown below. Fit a straight line through the data from 200 K to 400 K. | Temperature / K | Resistivity / 10⁻⁸ Ω m | | --- | --- | | 200 | 1.05 | | 300 | 1.73 | | 400 | 2.41 | Find the gradient, the fractional temperature coefficient at 300 K, and the intercept obtained by continuing that line to 0 K. The coefficient at 300 K is defined as (dρ/dT)/ρ(300 K).

Gradient dρ/dT / Ω m K⁻¹
Fractional temperature coefficient at 300 K / K⁻¹
Straight-line intercept at 0 K / 10⁻⁸ Ω m

A 500 m conductor must have resistance no greater than 0.20 Ω at 20 °C. Use these rounded design values. | Material | Resistivity / Ω m | Density / kg m⁻³ | | --- | --- | --- | | Copper | 1.72 × 10⁻⁸ | 8890 | | Aluminium | 2.83 × 10⁻⁸ | 2705 | For each material, calculate the minimum cross-sectional area and the mass at that area. The support allows a conductor mass of at most 120 kg; ignore joints, insulation and mechanical reinforcement when calculating mass.

Minimum copper area / mm²
Copper mass at that area / kg
Minimum aluminium area / mm²
Aluminium mass at that area / kg

A single-carrier strip is 2.0 mm wide and 0.10 mm thick. A current of 10 mA runs along its length. A 0.50 T magnetic field is normal to its wide face, and the measured Hall voltage magnitude across its width is 2.0 mV. Assume uniform current and carrier charge magnitude 1.60 × 10⁻¹⁹ C. Use |V_H| = BI/(n|q|t), where t is thickness along the magnetic field. Determine carrier density and drift speed.

Carrier number density / m⁻³
Drift speed / m s⁻¹

Practise

Practise after feedback: Solid State Physics

A text-first Solid State Physics assessment with labelled response controls.

About 10 minutes

Practise

Questions are selected when you start. Use the feedback to decide what to practise next; this does not prove mastery.

Recent attempts

History is stored only in this browser.

No completed attempts are saved yet.

This check needs JavaScript to record answers. The reviewed questions are listed below for study.

The Hall voltage across a slab of thickness $t$ (measured along the magnetic field) carrying current $I$ in field $B$ is $V_H=\dfrac{IB}{nqt}$. If the slab is replaced by one of the same material with twice the thickness, carrying the same current in the same field, what happens to $V_H$?

It halves.
It doubles.
It is unchanged because $n$ and $q$ are unchanged.
It quadruples.

Check my progress

Check my progress: Solid State Physics

A text-first Solid State Physics assessment with labelled response controls.

About 10 minutes

Check my progress

Answer 1 question. If accepted, this result can contribute to your course progress.

Recent attempts

History is stored only in this browser.

No completed attempts are saved yet.

Check again

Check again: Solid State Physics

A text-first Solid State Physics assessment with labelled response controls.

About 10 minutes

Check again

Answer 1 question. If accepted, this result can contribute to your course progress.

Recent attempts

History is stored only in this browser.

No completed attempts are saved yet.

Review

Review: Solid State Physics

A text-first Solid State Physics assessment with labelled response controls.

About 10 minutes

Review

Answer 1 question. A scheduled review can contribute to your course progress only when it is due and the result is accepted.

Recent attempts

History is stored only in this browser.

No completed attempts are saved yet.

How this activity affects progress

Course and syllabus information

Course: Advanced Physics
Edition: Advanced Physics

Solid State Physics

Revision

Practice

Check what I know: Solid State Physics

Starting check complete

Practise: Solid State Physics

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Practise after feedback: Solid State Physics

Practice complete

Check my progress: Solid State Physics

Progress check complete

Check again: Solid State Physics

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Review: Solid State Physics

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