If the diameter of a wire is sufficiently small, electrons will experiencequantum confinement in the transverse direction. As a result, their transverse energy will be limited to a series of discrete values. One consequence of this quantization is that the classical formula for calculating the electrical resistance of a wire, is not valid for quantum wires. Instead, an exact calculation of the transverse energies of the confined electrons has to be performed to calculate a wire's resistance. Following from the quantization of electron energy, the electrical conductance is found to be quantized in multiples of, where is the electron charge and is the Planck constant. The factor of two arises from spin degeneracy. A single ballisticquantum channel has a conductance equal to this quantum of conductance. The conductance is lower than this value in the presence of internal scattering. The importance of the quantization is inversely proportional to the diameter of the nanowire for a given material. From material to material, it is dependent on the electronic properties, especially on the effective mass of the electrons. Physically, this means that it will depend on how conduction electrons interact with the atoms within a given material. In practice, semiconductors can show clear conductance quantization for large wire transverse dimensions because the electronic modes due to confinement are spatially extended. As a result, their Fermi wavelengths are large and thus they have low energy separations. This means that they can only be resolved at cryogenic temperatures where the thermal energy is lower than the inter-mode energy separation. For metals, quantization corresponding to the lowest energy states is only observed for atomic wires. Their corresponding wavelength being thus extremely small they have a very large energy separation which makes resistance quantization observable even at room temperature. approximation for CNT, CNT and CNT
Carbon nanotubes
The carbon nanotube is an example of a quantum wire. A metallic single-walled carbon nanotube that is sufficiently short to exhibit no internal scattering has a conductance that approaches two times the conductance quantum,. The factor of two arises because carbon nanotubes have two spatial channels. The structure of a nanotube strongly affects its electrical properties. For a given nanotube, if n = m, the nanotube is metallic; if n − m is a multiple of 3, then the nanotube is semiconducting with a very small band gap, otherwise the nanotube is a moderate semiconductor. Thus all armchair nanotubes are metallic, and nanotubes,, etc. are semiconducting.
Applications
Electronic devices
Nanowires can be used for transistors. Transistors are used widely as fundamental building element in today's electronic circuits. One of the key challenges of building future transistors is ensuring good gate control over the channel. Due to the high aspect ratio, wrapping the gate dielectric around the nanowire channel, can result in good electrostatic control of channel potential, thereby turning the transistor on and off efficiently.
Sensing using semiconductor nanowires
In an analogous way to field-effect transistor devices in which the modulation of conductance in the device, is controlled by electrostatic potential variation of the charge density in the conduction channel, the methodology of a Bio/Chem-FET is based on the detection of the local change in charge density, or so-called “field effect”, that characterizes the recognition event between a target molecule and the surface receptor. This change in the surface potential influences the Chem-FET device exactly as a ‘gate’ voltage does, leading to a detectable and measurable change in the device conduction.
