elMickotanko said:
Is it not the other way round? I mean its heat that causes the vibrations of the atomic lattice, not the vibrations causing heat?
Its been a while since my devices class so i cant remember much.
elMickotanko:
Acute observation, yet not precise elMickotanko
(but indeed this kind of queries are what make things to be cleared up, and concepts to become solid and improved; thanks)
Heat transfer occurs by atomic lattice vibrations in solids. These vibrations can be broken down into the superposition of normal modes normal vibration. Through quantum mechanics and the wave-particle duality, these normal modes can be treated as particles. These particles are called phonons, which are in the class of particles called bosons. Lattice vibrations, and therefore phonons, travel at the speed of sound through a solid.
In thermodynamics and solid state physics,
the Debye model is a method developed by Peter Debye in 1912
for estimating the phonon contribution to the specific heat (heat capacity) in a solid.
It treats the vibrations of the atomic lattice (heat) as phonons in a box, in contrast to Einstein model, which treats the solid as many individual, non-interacting quantum harmonic oscillators. The Debye model correctly predicts the low temperature dependence of the heat capacity. Just like the Einstein model, it also recovers the Dulong-Petit law at high temperatures. But due to simplifying assumptions, its accuracy suffers at intermediate temperatures.
Following Planck’s idea on “energy quanta” originally applied to black-body radiation (1900), or according to the quantum mechanics founded by Heisenberg and Schr¨odinger (1925-26), physicists usually go forward as follows.
(1) Consider the lattice vibration as an infinite-dimensional system of harmonic oscillators.
(2) Decompose the system into independent simple harmonic oscillators, and calculate the distribution of vibration frequencies.
(3) Apply statistical mechanics to determine the macroscopic equilibrium state (the Gibbs state) of the quantized lattice vibration, and compute the internal energy U = U(T) (per unit cell) where T is the absolute temperature.
Then the specific heat is given by
C(T) =∂U/∂T
The surface relaxation effect and the local clamping effect are shown to be responsible for the specific heat of a small particle.
What you might refer to, and there you´re right it's about the amplitude of lattice vibration as a function of the temperature which is also calculated by the Debye model of a solid (Thermal Lattice Vibration).
For example, the wafer temperature during ion implantation is normally below 400 K, the lattice vibrations can influence the trajectories of the implanted ions.
Especially the probability for scattering an ion out of a channel (de-channeling) is increased by increasing the wafer temperature. Due to the fact that the knowledge of the atomic lattice behavior is required for the simulation it is necessary to apply a temperature dependent lattice vibration model.