A Quantum Confinement Effect and Density of States

[says]

I've been reading a bit about the quantum confinement effect on nanowires, particularly how it changes the band structure. I'm trying to find an explanation on why the density of states splits into sub-bands. At the moment all I'm running into is 'because of the quantum confinement effect' which is a really superficial explanation. Hoping someone can spread some light!

 

[Lord Jestocost]

"One of the most direct effects of reducing the size of materials to the nanometer range is the appearance of quantization effects due to the confinement of the movement of electrons. This leads to discrete energy levels depending on the size of the structure as it is known from the simple potential well treated in introductory quantum mechanics. Following this line artificial structures with properties different from those of the corresponding bulk materials can be created. Control over dimensions as well as composition of structures thus makes it possible to tailor material properties to specific applications."

From: "Quantum size effects in nanostructures" by Kjeld Pedersen
Quantum size effects in nanostructures - AAU

 

[says]

What causes the quantization though?

 

[ZapperZ]

What causes the quantization though?

Er... Back up a bit here. Let me ask you this. What causes the "quantization" in an infinite square well?

Zz.

 

[says]

Confinement of particles in a potential field

 

[ZapperZ]

Confinement of particles in a potential field

Or rather, to be more explicit, the boundary conditions as dictated by the potential field. So why should the confinement in these nanowires that resulted in the quantized behavior be puzzling to you?

Zz.

 

[says]

So boundary conditions cause quantisation of energy levels. In solids, it causes quantised energy bands. As we decrease the dimensions and size of something it approaches discrete energy levels (atomistic)