Title: Evolution of electron models

This module takes a look at the electrical and thermal properties of materials we analyzed in this course.

Starting from the classical Drude model and its implications, we add new concepts and move towards quantum mechanical descriptions to explain observed phenomena.

Each model has its implications, only some of which are actually true in reality.

1) Drude model:

This model describes electrons as classical particles that are separated from the ionic cores and do not interact with one another. However, they do collide with the ionic cores of the atoms.

Look at the implications of this model. Make sure you understand them and decide if they properly describe reality or not (i.e. they  are “true” or “false”).

Implications:

Q: Materials usually have an electrical resistivity [...] (usually)
A: true
Q: Hall coefficients are always negative [...]
A: false
Q: All electrons can have the same energy [...]
A: false
Q: Electronic heat capacity = 3/2 x kb x electron density [...]
A: false

2) QM free electrons + periodic boundary conditions + Pauli principle:

By looking at electrons as quantum mechanical particles (they hence obey the Schrödinger equation), applying boundary conditions (which leads to a quantization of energies) and applying the Pauli principle (which only allows for 2 electrons of the same energy), we arrive at a new picture.

Look at the implications of this model. Make sure you understand them and decide if they properly describe reality or not (i.e. they  are “true” or “false”).

Implications:

Q: Electrons are not allowed to have the same energy, so there is a highest occupied energy level EF [...]
A: true
Q: A system of electrons has a density of states [...]
A: true
Q: The DOS in 3D is proportional to sqrt(Energy) AND infinite (continues to grow when E --> infinity) [...]
A: false
Q: Correction of the electronic heat capacity because not all electrons can take up thermal energy [...]
A: true
Q: Hall coefficients are still negative [...]
A: false

3) Interaction of QM electrons with ionic cores: LCAO and Blochness of electron function:

By admitting that the interaction of electrons and the ionic cores cannot be ignored if we want to explain further important phenomena, we allow them to do so. LCAO and Blochness lead to a new picture (as seen in the lecture for the 1D atomic chain).

Look at the implications of this model. Make sure you understand them and decide if they properly describe reality or not (i.e. they  are “true” or “false”).

Implications:

Q: Existence of energy bands [...]
A: true
Q: Existence of band gaps and insulators [...]
A: true

4) Effective mass

By introducing the concept of the effective mass to the energy band picture, a new phenomenon is described.

Look at the implications of this model. Make sure you understand them and decide if they properly describe reality or not (i.e. they  are “true” or “false”).

Implications:

Q: Hall coefficients can be positive [...]
A: true