Introduction to Nano-materials. As part of ECE-758 – Introduction to Nanotechnology. Outline. What is “nano-material” and why we are interested in it? Ways lead to the realization of nano-materials Optical and electronic properties of nano-materials Applications . What is “nano-material” ?.
As part of ECE-758 – Introduction to Nanotechnology
SchrÖdinger equation in free-space:
Electron behavior: plane wave
SchrÖdinger equation in bulk semiconductor:
Electron behavior: Bloch wave
SchrÖdinger equation in nano-material:
with artificially generated extra potential contribution:
Quantum well – 1D confined and in parallel plane 2D Bloch wave
Quantum wire – in cross-sectional plane 2D confined and 1D Bloch wave
Quantum dot – all 3D confined
Electrons in semiconductors: highly mobile, easily transportable and correlated, yet highly scattered in terms of energy
Electrons in atomic systems: highly regulated in terms of energy, but not mobile
Electrons in semiconductors: easily controllable and accessible, yet poor inherent performance
Electrons in atomic systems: excellent inherent performance, yet hardly controllable or accessible
Electron in fully confined structure (QD with edge size d), its allowed (quantized) energy (E) scales as 1/d2 (infinite barrier assumed)
Coulomb interaction energy (V) between electron and other charged particle scales as 1/d
If the confinement length is so large that V>>E, the Coulomb interaction mixes all the quantized electron energy levels and the material shows a bulk behavior, i.e., the quantization feature is not preserved for the same type of electrons (with the same effective mass), but still preserved among different type of electrons, hence we have (discrete) energy bands
If the confinement length is so small that V<<E, the Coulomb interaction has little effect on the quantized electron energy levels, i.e., the quantization feature is preserved, hence we have discrete energy levels
Similar arguments can be made about the effects of temperature, i.e., kBT ~ E?
But kBT doesn’t change the electron eigen states, instead, it changes the excitation, or the filling of electrons into the eigen energy structure
If kBT>E, even E is a discrete set, temperature effect still distribute electrons over multiple energy levels and dilute the concentration of the density of states provided by the confinement, since E can never be a single energy level
Therefore, we also need kBT<E!
The critical size is, therefore, given by V(dc)=E(dc)>kBT (25meV at room temperature).
For typical III-V semiconductor compounds, dc~10nm-100nm (around 20 to 200 mono-layers).
More specifically, if dc<10nm, full quantization, if dc>100nm, full bulk (mix-up).
On the other hand, dc must be large enough to ensure that at least one electron or one electron plus one hole (depending on applications) state are bounded inside the nano-structure.