1D (Nanowire)

1D (Nanowire)

1. What 1D Means — Confined in Two Dimensions, Free in One

1D nanomaterial: confined to nanoscale in two dimensions (diameter $1$–$100$ nm) and long (microns–mm) in the third ⇒ wire geometry. Electrons free to move along length only, quantized in cross-section (2D confinement).

Examples: Si nanowire (dia 10 nm, length µm), Ag nanowire, carbon nanotube (CNT) (hollow 1D, dia 1 nm, length µm, actually rolled 2D), ZnO nanowire for sensors.

2. Electronic Structure — 1D Quantum Confinement

Cross-section acts as 2D particle-in-a-box → subbands:

Energy depends continuously on $k_z$ (along wire) but discrete steps across. Density of states $∝1/√E$ with van Hove singularities at subband edges (vs 0D delta, 2D step, 3D $√E$).

• Results in anisotropic transport: conduction along wire good, across not.

3. Properties and Differences from 0D

Feature	0D (Dot)	1D (Wire)
Confinement	3D (all)	2D (diameter)
States	discrete (0D, atom-like)	1D subbands with free $k_z$
Transport	hopping/tunneling	ballistic along length if $L$ < mean free path
Applications	QLED, bio-tags (light)	Interconnects, FET channel (nanowire transistor), sensors, transparent electrodes

4. Why Nanowires Matter

• Transistor: nanowire FET: gate wraps around wire ⇒ excellent electrostatics, sub-10 nm channel (e.g., Si nanowire gate-all-around).
• Sensors: huge surface-to-volume ⇒ single molecule detection (conductance changes ~10% per molecule adsorption).
• Mechanical: defect-free ⇒ very high strength (tensile ~10 GPa), flexible.
• Transparent conductor: Ag nanowire network replaces ITO for flexible displays (high conductivity + transparency vs brittle ITO).

5. Worked Illustration

Si nanowire dia 5 nm: confinement ΔE≈ h²/(8m* a²)≈0.1 eV ⇒ E_g effective ~1.22 eV (vs bulk 1.12) ⇒ slight blue shift but mainly transport remains 1D.

CNT dia 1 nm: quantized around circumference ⇒ metallic vs semiconducting depending on chirality (n,m).

6. Exam Points

• Define 1D as confined in two dimensions, free in one, give nanowire/nanotube example — 3-5 marks, very frequent (part of classification).
• Contrast 0D (fully discrete) vs 1D (subbands with $1/√E$ DOS) — 5 marks, frequent.
• Give two applications (transistor, sensor/transparent electrode) — 5 marks, very frequent.
• Mention diameter $1$–$100$ nm, length µm–mm — 3 marks.