Carbon nanotubes (CNTs) exhibit remarkable electrical properties that are intrinsically linked to their chiral structure, making them highly attractive for nanoelectronics applications. The chirality of a CNT, defined by the roll-up vector (n,m) of the graphene sheet, determines whether the tube behaves as a metal or a semiconductor. Armchair nanotubes, where n = m, are always metallic with zero bandgap, while zigzag (n,0) and chiral (n ≠ m) nanotubes can be either semiconducting or metallic depending on their indices. The bandgap of semiconducting CNTs inversely correlates with their diameter, following the relation Eg ≈ 0.9 eV/d (nm), enabling tunable electronic properties through structural control.

Metallic CNTs demonstrate exceptionally high electrical conductivity, with theoretical predictions suggesting ballistic transport at room temperature over micrometer lengths. Measurements have shown conductance approaching the quantum limit (4e²/h), with mean free paths exceeding 1 μm in defect-free tubes. The one-dimensional nature of CNTs leads to quantized conductance, where current flows through discrete electron channels. Armchair nanotubes exhibit nearly perfect transmission of electron waves, resulting in resistances as low as 6.45 kΩ per channel. In contrast, semiconducting CNTs display field-effect mobilities surpassing 100,000 cm²/Vs, significantly higher than traditional silicon channels.

The unique band structure of CNTs arises from the quantization of electron motion around the tube circumference. Metallic tubes show linear dispersion at the Fermi level, while semiconducting tubes exhibit parabolic dispersion with size-dependent bandgaps. For example, a (10,0) zigzag nanotube with 0.78 nm diameter demonstrates a bandgap of approximately 1.1 eV, comparable to silicon but with superior carrier transport. The absence of surface dangling bonds and strong covalent bonding along the tube axis contribute to the exceptional electronic properties, including high current-carrying capacities exceeding 10⁹ A/cm².

In field-effect transistors (FETs), semiconducting CNTs serve as high-performance channels. Top-gated CNTFETs have demonstrated subthreshold swings below 70 mV/decade, approaching the thermodynamic limit. The cylindrical gate geometry provides excellent electrostatic control, suppressing short-channel effects in devices with channel lengths below 10 nm. High-performance n-type and p-type CNTFETs have been realized using appropriate contact metals and doping strategies, with on/off ratios exceeding 10⁶ and transconductance values over 40 μS/μm. Complementary metal-oxide-semiconductor (CMOS) circuits built from CNTs have shown switching frequencies in the gigahertz range, validating their potential for digital logic applications.

For interconnect applications, metallic CNTs offer solutions to the resistivity scaling challenges faced by copper in advanced technology nodes. Bundles of parallel CNTs can achieve current densities over 10⁷ A/cm² without electromigration failure, compared to copper's limit of approximately 10⁶ A/cm². The temperature coefficient of resistance in metallic CNTs is nearly zero, unlike copper which suffers from increased resistivity at higher temperatures. Three-dimensional CNT interconnects have demonstrated reduced RC delays by 30% compared to copper at the 10 nm scale, with contact resistances below 10 kΩ per tube being achieved through optimized interface engineering.

Flexible electronics benefit from CNTs' mechanical robustness combined with their electrical performance. CNT networks maintain conductivity even under bending radii below 1 mm, with strain-dependent resistance changes below 5% after thousands of bending cycles. Transparent conductive films using CNTs have achieved sheet resistances of 100 Ω/sq at 90% transparency, competing with indium tin oxide in flexible displays and touch sensors. The piezoresistive effect in CNTs enables strain sensors with gauge factors over 100, significantly higher than metal foil gauges.

Quantum transport phenomena dominate in CNT-based devices at nanoscale dimensions. At low temperatures, clear conductance quantization steps are observed corresponding to the number of available conduction channels. The four-fold degeneracy (two spin states and two subbands) in metallic CNTs leads to quantized conductance in multiples of 4e²/h. Phase-coherent transport lengths exceed 300 nm at room temperature, enabling interference effects such as Fabry-Pérot oscillations in short tubes. The Luttinger liquid behavior observed in long CNTs manifests as power-law dependence of conductance on temperature and voltage.

Ballistic conduction in short CNT channels presents both opportunities and challenges. While ideal ballistic transport would eliminate energy dissipation in the channel, real devices face significant contact resistance barriers. The Schottky barrier at metal-CNT interfaces often limits current injection, with measured contact resistances ranging from 5 to 50 kΩ depending on the metal work function and tube diameter. Palladium and rhodium contacts have shown particular promise for low-resistance p-type contacts, while scandium and ytterbium work well for n-type devices. Contact resistance scaling remains a critical challenge, as the quantum resistance of individual tubes becomes comparable to or larger than the contact resistance in optimized systems.

The one-dimensional nature of CNTs leads to pronounced electron-electron interactions and strong correlation effects. Coulomb blockade phenomena are readily observed in short CNT segments at low temperatures, with charging energies reaching 10 meV for tubes shorter than 100 nm. The interplay between quantum confinement and electron interactions gives rise to exotic phenomena such as Wigner crystallization and spin-charge separation in carefully engineered structures. These effects are being explored for quantum information applications, including spin qubits and valleytronic devices.

Manufacturing challenges for CNT-based electronics include achieving pure semiconducting or metallic tube populations, precise alignment, and reproducible contact formation. Density gradient separation and selective destruction techniques have enabled semiconductor purity levels above 99.9%, essential for large-scale integration. Directed assembly techniques using dielectrophoresis or chemical patterning have demonstrated alignment accuracies within ±1° over centimeter scales. The development of end-bonded contacts, where the metal directly bonds to the tube ends rather than sidewalls, has reduced contact resistances by an order of magnitude compared to conventional side contacts.

Looking forward, the integration of CNTs with emerging device architectures such as gate-all-around transistors and three-dimensional integrated circuits presents new opportunities. The compatibility of CNTs with low-temperature processing enables their integration on flexible substrates and monolithic three-dimensional circuits. Heterostructures combining CNTs with two-dimensional materials like graphene and transition metal dichalcogenides are being explored for novel device functionalities. As fabrication techniques mature, CNT-based electronics are progressing from discrete devices to full system-level demonstrations, including microprocessors and analog-to-digital converters.

The electrical properties of CNTs continue to inspire innovations across multiple domains of nanoelectronics. From ultra-scaled transistors to quantum coherent devices, the unique combination of dimensionality, symmetry, and material properties positions CNTs as a versatile platform for exploring new physics and enabling technological advancements beyond conventional semiconductor roadmaps. Ongoing research focuses on overcoming the remaining manufacturing and integration challenges while harnessing the full potential of their exceptional electrical characteristics.