Lesson 1: Mesoscopic physics and nanotechnology

Lesson 1:

Mesoscopic physics and nanotechnology

Average Cost per Transistor vs Time

100 n$

MOSFET Feasibility

Physical limits

… undesired effects impact

severely MOSFET performances

… undesired effects impact

severely MOSFET performances

Short Channel Short

Channel Direct

Tunnelling Direct

Tunnelling

Statistical Fluctuations Statistical Fluctuations

Technological Limit

Nano – Era

Economic Limit

Conductance of one-dimensional ballistic wire is quantized:

I V

G =

/

= 2*2e

/h

Quantum of resistance:

h/e² = 25 kOhm With perfect contacts:

(two subbands in NT)

Mesoscopic regime

?

nm mm

Nanoscale electrical transport

Charge -e Electrons

Wave function

Single-electron effects

Size quantization

Mesoscopic transport; quantum transport ...

Resistance and conductance

Ohm’s first law: V = R . I

Ohm’s second law: R = V / I [W]

Bulk materials; resistivity r:

R = r L / A

Nanoscale systems (coherent transport):

R is a global quantity, cannot be decomposed into local resistivities (see why later)

Conductance G: G = 1 / R = I / V [unit e²/h]

(Not conductivity s)

R is additive A

L r

Transport regimes

• Ballistic transport, L << L_m, L_f

– no scattering, only geometry (eg. QPC)

– when l_F~ L: quantized conductance G~e²/h

• Diffusive, L > L_m

– scattering, reduced transmission

• Localization, L_m << L_f << L

– R ~ exp(L) due to quantum interference at low T

• Classical (incoherent), L_f, L_m << L

– ohmic resistors

Length scales: l_F Fermi wavelength

(only electrons close to Fermi level contribute to G) L_m momentum relaxation length (static scatterers) L_f phase relaxation length (fluctuating scatterers) L sample length

(simplified)

Electronic structure

Density of states (DOS) ^1D:semiconductor quantum wires conducting polymers nanotubes

0D:

atoms molecules nanocrystals

metal nanoparticles quantum dots short nanotubes

A short digression: Nanostructures and

fabrication technologies

Ideas at the basis of the nanolitography (x-ray litography, electron beam litography. Top- down)

N. B.

Minimum size >20 nm

Spatial order on a large scale

Ideas at the basis of the nanoimprinting litography ( Top-down)

Growth of nano-object on prepatterned surface (Hybrid top-down/bottom-up)

Au

Clusters and colloids ( bottom-up)

Fullerens and carbon nanotubes ( bottom-up)

Nanowires ( top-down and bottom-up)

- Single nanostructure system

Source

Drain

Metallic nanocluste

Fundamental rs

paramaters:

1)Material;

2)Shape;

3)Size;

4)Surrounding.

- Nanostructures array systems: artificial atoms solids

Electronic coupling (wavefunctions

overlapping, capacitive coupling, electron- electron interactions

Structural disorder:

site-to-site energy fluctuatiuons

Fundamental paramaters:

1)Material;

2)Shape;

3)Size;

4)Surrounding;

5)Electronic coupling;

6)Structural disorder.