Nanowires

Nanowires are quasi one-dimensional crystals with a cylindrical shape, length varying from several microns (1e-6 m) to just several nanometers (1 nm = 1e-9 m) and diameters usually less than 100 nm. They are made of semiconductor materials such as silicon (Si) or gallium-arsenide (GaAs), oxides like zinc-oxide (ZnO) and metals.

There are two approaches to the growth of nanowires: bottom-up and top-down. Top-down relies on externally controlled tools used to shape the nanowires, while bottom-up is based on intrinsic properties of the materials to self-assembly. Examples of bottom-up growing techniques are vapor-liquid-solid (VLS) mechanism or template-based synthesis. A top-down approach is lithography.

Nanowires are promising materials for many applications, not only because of their geometry but also because they possess unique physical properties.

Nanowire field-effect transistors

A nanowire field-effect transistor (NWFET) is an electronic device which can act as a normal transistor. As such, it has a channel which consists of a nanowire through which the electrons can flow form the source to the drain contacts. A coaxial gate electrode, separated from the channel by an oxide layer, controls the amount of current. The geometry of a NWFET can be seen in the following picture.

nwfet

Single-electron transistor

A NWFET can also behave as a single-electron transistor (SET) in the Coulomb blockade regime at low enough temperatures. In this regime the following effect occurs. The energy needed for an electron to occupy the channel is much higher than its thermal energy, therefore the electron cannot enter into the channel and the device is blocked. No current flows through it and it contains a integer number N of electrons. Hence the name of Coulomb blockade regime.

Nevertheless, the gate voltage can move up and down the energy levels inside the channel. In the case where one of these levels (empty) lies in the energy window defined by the Fermi levels of the contacts (the source to drain voltage), the state of the channel can fluctuate between N and N+1 electrons and a significant current can pass through the NWFET. The device is thus termed SET because of its sensitivity to single-electron Coulomb charging effects.

Coulomb diamonds

Typical of this regime are certain structures with the shape of diamonds that arise in the stability diagrams, which represent the source to drain current as a function of gate and source to drain voltages. These structures are called Coulom diamonds. To be able to simulate them, the model has to be able to account for few-electron Coulomb charging effects. A mean-field approximation for the interaction between electrons cannot describe these effects and models based on it fail to produce Coulomb diamonds. One can see the appearance of simulated Coulomb diamonds in the following graph.

diamonds

In this stability diagram current is represented by colors, from minimum (black) to maximum (white) current, passing through blue, red, orange and yellow. In each of the diamonds the channel of the NWFET is occupied by an integer number of electrons, being N=1 in the leftmost diamond and N=3 in the rightmost diamond. And current is blocked (black color). Outside these regions current can flow.

State of the art in NWFET modelling

There are several approaches to the simulation of electronic transport in a NWFET, corresponding to different regimes of operation and aspects of the device. Each approach is valid in a certain domain or context, be it high or low temperature, large or small size of the device. Even studies focused on other kind of systems can be useful to the understanding of NWFETs, such as quantum dots.

Many of the approaches are usually hybrid models that combine different techniques.