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Electronic, magnetic and optical materials

Check the basics of band theory, the conductivity of metals and semiconductors, Matthiessen's rule, the Hall effect, ferromagnetism and hysteresis, soft and hard magnetic materials, and refraction, absorption and emission with multiple-choice questions.

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Electronic, magnetic and optical materials: key points

The electrical properties of materials can be understood through band structure. Metals conduct well because there are continuous empty levels at the Fermi level, and their resistivity increases with temperature as scattering by lattice vibrations grows. In semiconductors, doping can change the conductivity σ = neμ enormously, and in the intrinsic regime the resistivity falls as temperature rises. The resistivity of metals is split into lattice-vibration and impurity components by Matthiessen's rule.

Ferromagnets have a spontaneous magnetization below the Curie temperature, and the shape of the hysteresis loop determines their applications. Soft magnetic materials with low coercivity are used for transformer and motor cores, and hard magnetic materials with high coercivity for permanent magnets. Among optical properties, the refractive index and reflectance, the absorption coefficient, and the difference between direct and indirect transitions are important.

All Electronic, magnetic and optical materials questions (12)
  1. Which value is closest to the resistivity of n-type silicon with a donor concentration of 1.0×10¹⁶ cm⁻³ (room temperature, all donors ionized)? Take the electron mobility as 1350 cm²/(V·s) and the elementary charge as 1.60×10⁻¹⁹ C, and neglect the hole contribution.
  2. Which correctly describes how electrical resistivity changes when the temperature is raised? Assume the semiconductor is in the intrinsic regime.
  3. The resistivity of pure copper due to lattice vibrations is 1.70 µΩ·cm at 300 K and 0.20 µΩ·cm at 77 K. For a copper alloy in which added impurities give a temperature-independent residual resistivity of 0.40 µΩ·cm, which value is closest to the resistivity ratio ρ(300 K)/ρ(77 K) according to Matthiessen's rule?
  4. Magnesium has two valence electrons, and the band formed from 3s orbitals is exactly filled by two electrons per atom. Which correctly explains why magnesium is nevertheless a metal?
  5. Which correctly describes what can be learned from Hall effect measurements?
  6. When ferromagnetic iron is heated above its Curie temperature (about 770 °C), what happens to its magnetism?
  7. Which correctly describes a soft magnetic material suitable for a transformer core?
  8. The area of the hysteresis loop of a core material (the loss per cycle) is 50 J/m³. Which value is closest to the hysteresis loss when a core of volume 0.010 m³ is used at 50 Hz AC?
  9. When an external magnetic field is applied to a demagnetized ferromagnet and gradually increased, which correctly describes how magnetization proceeds?
  10. When light from air strikes the surface of a transparent material with a refractive index of 2.4 (close to diamond) at normal incidence, which value is closest to the reflectance at the surface? Neglect absorption.
  11. Light is shone on a 1.0 µm thick film of a material with an absorption coefficient of 1.0×10⁴ cm⁻¹. Which value is closest to the fraction of light transmitted through the film? Neglect surface reflection and take I = I₀exp(−αx).
  12. What is the main reason silicon is hardly ever used as the emitting material in light-emitting diodes?

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