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Thin films, surfaces and nanomaterials

Learn surface energy, homogeneous and heterogeneous nucleation and the critical nucleus radius, thin-film growth modes, thermal stress in films, and the characteristics of nanomaterials such as specific surface area and the quantum size effect with multiple-choice questions.

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Thermal expansion and stress →

Thin films, surfaces and nanomaterials: key points

Atoms at surfaces and interfaces have lost some of their bonds and so carry excess energy (surface energy and interfacial energy). When a nucleus of a new phase forms, the decrease in volume free energy competes with the increase in interfacial energy, and only nuclei larger than the critical radius r* = −2γ/ΔGv grow. Heterogeneous nucleation on substrates and walls has a lower energy barrier.

Thin films grow in layer-by-layer, island, or layer-then-island modes, depending on the balance of surface energies and the lattice mismatch. The difference in thermal expansion from the substrate produces a thermal stress σ = EΔαΔT/(1 − ν), which causes bowing, delamination and interconnect failures. Making particles nanosized increases the specific surface area, and the quantum size effect and Ostwald ripening become prominent.

All Thin films, surfaces and nanomaterials questions (12)
  1. Which statement about the surface energy of metal crystals is correct?
  2. In homogeneous nucleation, take the free energy change on forming a spherical nucleus of radius r as ΔG = (4/3)πr³ΔGv + 4πr²γ. For an interfacial energy γ = 0.10 J/m² and a free energy change per unit volume ΔGv = −2.0×10⁸ J/m³, which value is closest to the critical nucleus radius r*?
  3. In heterogeneous nucleation, with θ the contact angle between nucleus and substrate, the energy needed to form a critical nucleus is f(θ) = (2 + cosθ)(1 − cosθ)²/4 times that for homogeneous nucleation. Which value is closest to f(θ) for θ = 60°?
  4. At the same undercooling, how does the radius of curvature of the critical nucleus in heterogeneous nucleation compare with the critical nucleus radius in homogeneous nucleation?
  5. Among thin-film growth modes, which correctly describes Stranski–Krastanov (SK) growth?
  6. Let γs be the surface energy of the substrate, γf that of the film and γi the film–substrate interfacial energy. Under which condition is island (Volmer–Weber) growth likely?
  7. An aluminum film (Young's modulus 70 GPa, Poisson's ratio 0.35, linear thermal expansion coefficient 23×10⁻⁶ K⁻¹) on a silicon substrate (linear thermal expansion coefficient 2.6×10⁻⁶ K⁻¹) is cooled from a stress-free 125 °C to 25 °C. Assuming the substrate is sufficiently thick, what are the sign and magnitude of the thermal stress in the film, σ = EΔαΔT/(1 − ν)?
  8. A thermal oxide film (SiO₂, linear thermal expansion coefficient about 0.5×10⁻⁶ K⁻¹) is grown on a silicon substrate at high temperature and cooled to room temperature. Taking the linear thermal expansion coefficient of silicon as about 2.6×10⁻⁶ K⁻¹, what stress develops in the oxide film due to the difference in thermal expansion?
  9. When the diameter of spherical particles is reduced from 1 µm to 10 nm, by what factor does the surface area per unit volume (specific surface area) increase?
  10. How does the color of emission change when the size of semiconductor nanocrystals (quantum dots) such as CdSe is reduced?
  11. What is the main reason vacuum evaporation is carried out in high vacuum (for example, around 10⁻⁴ Pa)?
  12. When an alloy containing dispersed precipitate particles of different sizes in a matrix is held at high temperature for a long time, which correctly describes Ostwald ripening?

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